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AIP conference proceedings

Bell-state generation in circuit QED via Landau-Zener tunneling

Peter Hänggi A, Martijn Wubs, Sigmund Kohler, Keiji Saito, Yōsuke Kayanuma

Published Jan 1, 2007• 1 citation
Publisher

Abstract

A qubit may undergo Landau‐Zener transitions due to its coupling to one or several quantum harmonic oscillators. First we show that for a qubit coupled to one oscillator, Landau‐Zener transitions can be used for single‐photon generation and for the controllable creation of qubit‐oscillator entanglement, with state‐of‐the‐art circuit QED as a promising realization. Second, for a qubit coupled to two cavities, we show that Landau‐Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. Finally, for a qubit coupled to an environment or bath we propose to employ dissipative Landau‐Zener sweeps of the qubit for the detection of bath properties. At the heart of our proposals lies the calculation of the exact Landau‐Zener transition probability for the qubit, by summing all orders of the corresponding series in time‐dependent perturbation theory.

DOI
10.1063/1.2759729

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A qubit may undergo Landau‐Zener transitions due to its coupling to one or several quantum harmonic oscillators. First we show that for a qubit coupled to one oscillator, Landau‐Zener transitions can be used for single‐photon generation and for the controllable creation of qubit‐oscillator entanglement, with state‐of‐the‐art circuit QED as a promising realization. Second, for a qubit coupled to two cavities, we show that Landau‐Zener sweeps of the qubit are well suited for the robust creation of entangled cavity states, in particular symmetric Bell states, with the qubit acting as the entanglement mediator. Finally, for a qubit coupled to an environment or bath we propose to employ dissipative Landau‐Zener sweeps of the qubit for the detection of bath properties. At the heart of our proposals lies the calculation of the exact Landau‐Zener transition probability for the qubit, by summing all orders of the corresponding series in time‐dependent perturbation theory.
We demonstrate quantum control and entanglement generation using a Landau-Zener beam splitter formed by coupling two transmon qubits to a superconducting cavity. Single passage through the cavity-mediated qubit-qubit avoided crossing provides a direct test of the Landau-Zener transition formula. Consecutive sweeps result in Landau-Zener-Stückelberg interference patterns, with a visibility that can be sensitively tuned by adjusting the level velocity through both the nonadiabatic and adiabatic regimes. Two-qubit state tomography indicates that a Bell state can be generated via a single passage, with a fidelity of 78% limited by qubit relaxation.
We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.
We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
We propose a scheme to implement quantum information transfer between Cooper-pair boxes (CPBs) in a circuit quantum electrodynamic (QED) system with Landau—Zener tunneling. The system consists of two CPB qubits and a one-dimensional transmission line resonator (TLR). By analytically solving the eigenequation and numerically calculating the transition probability, the results show the quantum state transfer from one qubit to another via a fast adiabatic passage. The coupling mechanism is robust against decoherence effects.
An entangled state generation protocol for a system of two qubits driven with an ac signal and coupled through a resonator is introduced. We explain the mechanism of entanglement generation in terms of an interplay between unitary Landau-Zener-Stuckelberg (LZS) transitions induced for appropriate amplitudes and frequencies of the applied ac signal and dissipative processes dominated by photon loss. In this way, we found that the steady state of the system can be tuned to be arbitrarily close to a Bell state, which is independent of the initial state. Effective two-qubit Hamiltonians that reproduce the resonance patterns associated with LZS transitions are derived.